A cooling apparatus for an engine is per se known that cools the cylinder block and the cylinder head of the engine separately, that includes two cooling conduits communicated to an EGR cooler, and that changes the cooling paths employed for cooling the EGR cooler by operating valves, one provided in each of the cooling conduits (refer to Patent Document #1). Moreover, Patent Document #2 is a reference that is considered to have some relevance to the present invention.